1. Field of the Invention
This invention relates to tunable filters and more particularly to phase-locked loop filters having a closed-loop transfer function of the third order or above.
2. Description of the Prior Art
There exists a need in communication and radar frequency generation subsystems for "clean-up" tracking filters. Typically the frequency to be filtered, f.sub.0, is contaminated with interfering frequencies that have a fixed frequency spacing relative to f.sub.0. Furthermore, the entire spectrum can shift although the relationship between the desired output frequency and the interfering frequency is fixed. The solution calls for a narrow-band filter that can be tuned over the range of frequency variation.
Of the passive filter possibilities, crystal filters have the required narrow bandwidth and low insertion loss, but making them electronically tunable is not practical now. Phase-locked loops offer the practical solution to this filtering problem and are extensively used for this purpose. A general discussion of phase-locked loops is found in a publication entitled "Phase-Locked Loops" by S. C. Gupta, Proceedings of the IEEE, Vol. 63, No. 2, February 1975 pp. 291-306. As described in Gupta a phase-locked loop comprises a phase detector, amplifier, loop filter, and voltage controlled oscillator coupled in series with the output fed back to the input. The characteristics of the phase-locked loop are determined by the closed-loop transfer function that relates the phase of the input signal to the phase of the output signal. If the phase detector and voltage controlled oscillator are assumed linear, then a closed-loop transfer function may be expressed by equation (1), where s is the Laplace operator, K is a constant, and F(s) is the transfer function of the loop filter. EQU H.sub.c (s)=.PHI..sub.o (s)/.PHI..sub.i (s)=KF(s)/(s+KF(s))(1)
The power of s in the denominator of the closed-loop transfer function H.sub.c (s) determines the order of the phase-locked loop (e.g., first, second, third, etc.).
Normally, when a narrow-bandwidth tracking filter is needed, a second-order loop is selected, because this system remains stable, independent of the open-loop gain value and acquires lock reliably within the loop capture range. Unfortunately the second-order phase-locked loop does not provide enough attenuation close to the passband to adequately suppress unwanted frequencies. Prior higher-order loops such as a third-order loop may substantially outperform the second order loop but it is more complicated and harder to analyze and can become unstable as indicated on page 73 in a book entitled "Phaselock Techniques" by F. M. Gardner published in 1966 by John Wiley & Sons, Inc.
Higher-order all-pole phase-locked loops such as a sixth-order phase-locked loop are discussed in a book entitled "Frequency Synthesis: Techniques and Applications" by J. Gorski-Popiel, IEEE Press, New York, N.Y. in chapter 4 at pp. 111-116, but he does not address the narrow-band, tunable filter problem.
The objections to higher-order loops arise because the loop is usually used in the receiver where the signal-to-noise ratio is small. In this case the open-loop gain may change drastically because of the variation attributed to the noise, yielding the undesirable possibility of an unstable system. However, there are applications where the phase-locked loop is used in both Frequency Synthesizers and the System Modulator. Here the signal-to-noise ratio is high and the open-loop gain remains essentially constant. It is to these applications that this invention is particularly directed.
It is desirable to provide a phase-locked loop filter having a third or higher order transfer function to provide more attenuation close to the passband without upsetting the phase margin or the acquisition characteristic. It is essential to realize that the order of the loop is defined herein by the highest power of the Laplace operator s in the denominator of the closed-loop transfer function. The higher-order loops considered in this invention exhibit an open-loop magnitude response variation of -20 dB/decade over the frequency range where the open-loop magnitude response is greater than unity. Therefore, the higher order loops considered herein exhibit the acquisition characteristic of a first order loop. Thus the acquisition of these loops presents no problem.
It is desirable to provide a simple synthesis procedure for the loop filter of a phase-locked loop filter apparatus to realize a closed-loop transfer function with finite transmission zeros for specific values of .omega.. The finite transmission zero may be represented in the s-plane by zeros located in the j.omega. axis.
It is desirable to provide a phase-locked loop having a transfer function that corresponds to or duplicates a known optimized filter response such as an elliptic filter response.
It is further desirable to have a tunable filter with highly selective frequency characteristics such as the Cauer (elliptic); i.e. Chebyshev passband and stop-band attenuation, or the maximally-flat delay filter response with Chebyshev stop-band attenuation implemented by inserting a loop filter having circuit components of selected values and interconnected to form a unique loop filter transfer function in a phase-locked loop to provide the known filter response.